Linear Regression

Linear Regression. Fit the line y = mx + b to linear data where:
  1. x is the dependent variable
  2. y is the independent variable
  3. xi is the x value for i'th data point
  4. yi is the y value for the i'th data point
  5. N is the number of different standards are used
  6. yave is the average of the y values for the standards
  7. xave is the average of the x values for the standards.
This method assumes that there is no variance in the value for x and that each standard is analyzed once.

  1. Calculate Sums:

  2. Calculate Slope and Intercept:

  3. Uncertainty in Regression. Assuming linear function and no replicates, the standard deviation about the regression is:

  4. Uncertainty in ypredicted.

  5. Uncertainty in xpredicted. For an unknown with an average signal yunk from M replicates: